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Math Help - Square of an exponential function: simpler form?

  1. #1
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    Square of an exponential function: simpler form?

    It's part of a quantum course, but the problem I'm having is pretty straight math.

    There are two similar functions I need to square. I can do it fine, but the question calls for 'simplified form' and I'm struggling to simplify.

    They are 1-e^{-iat} and 1+e^{-iat}. Take the subtraction example (the only difference with the other one is a sign): I get 1-2e^{-iat}+e^{-2iat}.

    Is there a way to express this more simply?
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  2. #2
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    Re: Square of an exponential function: simpler form?

    Use [TEX] ... [/TEX] tags instead of [tex] ... [/tex] tags.

    Edit: Looks like you already did.
    Last edited by emakarov; September 20th 2011 at 11:57 AM.
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  3. #3
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    Re: Square of an exponential function: simpler form?

    Quote Originally Posted by Bravus View Post
    Is there a way to express this more simply?
    Not really. You can factor out e^{-iat} from the last two terms, but this is not much simpler.
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  4. #4
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    Re: Square of an exponential function: simpler form?

    Thanks very much. Guess I'll check with the tutor tomorrow and see whether they had something in mind, but it's reassuring that at least I wasn't just missing something simple. ;-)

    Thanks again.
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  5. #5
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    Re: Square of an exponential function: simpler form?

    AAaahh. Just to wrap up the question in case anyone else has a similar one.

    My mistake was that in quantum mechanics 'squaring' is actually (sometimes) shorthand for multiplying something by its complex conjugate, rather than simply by itself. I needed to multiply (1-e^{-iat}) by (1-e^{iat})... and *that* does get simpler, particularly with some judicious application of Euler's identity.

    Thanks again.
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